The depth, $h$ metres, of an underwater research drone exploring a lake is modelled by a function $h (t)$ , where $t > 0$ is the time in seconds after it passes a specific underwater marker.

The vertical acceleration of the drone is given by the equation

\frac{10}{\sqrt{t^3}} + 12t^2

A point $P (1, 5)$ lies on the depth-time curve.

Given that the rate of change of depth $h^{'} (t) = - 2$ at point $P$ ,

find the equation of the normal to the curve at $P$ , writing your answer in the form $h = m t + c$ , where $m$ and $c$ are constants,

determine an expression for $h (t)$ .

The depth, $h$ metres, of an underwater research drone exploring a lake is modelled by a function $h (t)$ , where $t > 0$ is the time in seconds after it passes a specific underwater marker.

The vertical acceleration of the drone is given by the equation

\frac{10}{\sqrt{t^3}} + 12t^2

A point $P (1, 5)$ lies on the depth-time curve.

Given that the rate of change of depth $h^{'} (t) = - 2$ at point $P$ ,

find the equation of the normal to the curve at $P$ , writing your answer in the form $h = m t + c$ , where $m$ and $c$ are constants,

determine an expression for $h (t)$ .

1.8 Integration

Question 27

Markscheme

1.8 Integration

Question 27

Markscheme

1.8 Integration

Question 27

1.8 Integration Questions

1.8 Integration

Question 27

1.8 Integration Questions